Question

Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was $5,000 more than twice the amount she put into the CD. How much did she invest in each account? Call the amount that Daniela invested in the CD d and the amount she invested in bonds b.

Answer 1

The amount invested in bonds = 35,000

The amount invested in CD = 15,000.

Explanation:

The total amount that Daniela invested is $50,000, this means if we call the amount invested in bonds
`b`, and the amount invested in CD
`d`, then we have:

`b+d=50,000` this says the total amount Daniela invested is $50,000.

And since the amount invested in bonds
`b` is $5,000 more than twice the amount Daniela put into the CD, we have:

`b=5,000+2d`.

Thus, we have two equations and two unknowns
`b` and
`d`:

(1).
`b+d=50,000`

(2).
`b=5,000+2d`,

and we solve this system by substituting
`b` from the second equation into the first:

`b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}`

or, the amount invested in CD is $15,000.

With the value of
`d` in hand, we now solve for
`b` from equation(2):

`b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}`

or, the amount invested in bonds is $35,000.